a. Are the quadratic terms important? Consider a linear model of LNEXPENSES on 12 explanatory variables. For the explanatory variables, include assets, GROUP, both versions of losses and gross premiums, as well as the two BLS variables. Also include the square each of the two loss and the two gross premium variables. Test whether the four squared terms are jointly statistically significant, using a partial \(F\)-test. State your null and alternative hypotheses, decision-making criterion, and decision-making rules.

b. Are the interaction terms with GROUP important? Omit the two BLS variables, so that now there are 11 variables, assets, GROUP, both versions of losses and gross premiums, as well as interactions of GROUP with assets and both versions of losses and gross premiums. Test whether the five interaction terms are jointly statistically significant, using a partial \(F\)-test. State your null and alternative hypotheses, decision-making criterion, and decision-making rules.

c. You are examining a company that is not in the sample with values LOSSLONG \(=0.025\), LOSSSHORT \(=0.040\), 

GPWPERSONAL \(=\) \(0.050, \mathrm{GPWCOMM}=0.120, \mathrm{ASSETS}=0.400, \mathrm{CASH}=0.350\), and GROUP \(=1\). Use the 11-variable-interaction model in part (b) to produce a \(95 \%\) prediction interval for this company.